Jun 13, 2019

Lifetime Consumption Utility with addition of trend following-like behavior

This post is going to get very abbreviated treatment since I am headed out to a Daughter's graduation.  In the last post Having Some Fun with Portfolio Choice vs. Lifetime Consumption Utility I was playing around with portfolio choice, spending, and consumption utility.  At the end of that post I wondered what would happen if we added a trend-following-like behavior.  Well, I took a shot at that question, though keep in mind none of this is real; it is highly highly FAKE.

If we were to hypothesize adding a third asset to our two asset portfolio -- and don't ask what or how much, this is just a hypothetical and I am interested in the behavior or movement more than I am the execution or plausibility -- we could re-envision the (old fake) efficient frontier in the last post like this (new fake) one where for the same level of return the vol shifts left but less on the safe end and more on the risk end. If I haven't mentioned it, the exact shift comes from only my imagination:


Figure 1. What adding a trend following allocation might do to an eff frontier???

From my imagination, yes, but the CME had a paper on Managed futures that had a graph almost exactly like this one except that the return assumptions were from 2005, so high, and their line shifted up a little, in addition to left, and it flattened at the top. But we are close enough for brainstorming purposes. 


IF we believe that feat of imagination, and IF we were to inherit the same setup as the last post, and IF we don't dwell on the nitty gritty charting and analytics (maybe when I get back or if there is popular demand, which I'm guessing there won't be), then the overall effect of doing this can be seen in the dreaded 3D surface form and would look like this where the blue surface is the last post and the colored surface on top is the one coming off the adjusted frontier:




The overall optima have not moved much, thought  that is hard to see here. The highest spend rates were nudged a bit towards 4% from 3.8% in the middle allocations although that 3.8 to 4.0 spend range is now serviced by "increments" 5 to 9 or what, in the original would have been allocations to risk from 40-90%. Before, 3.8 was only serviced by increments 6 and 7. 

The biggest change is that if one were to want to irrationally spend a little more (>4%, say 5%), and if one believes the EF I ginned up, then the new Trend allocation strategy at mid-to-high risk levels is a little friendlier than it was before. A pretty big gap is opening up on the front corner where high spend and high risk meet. 





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